Understanding the Valence Quark Structure of the Pion through GTMDs

Abstract: We investigate the internal structure of the pion using generalized transverse momentum-dependent parton distributions (GTMDs) within the light-cone quark model. By solving the quark-quark correlator, we derive the twist-$2$, $3$, and $4$ quark GTMDs in terms of light-front wave functions (LFWFs). Out of the $16$ possible GTMDs, $12$ are found to be nonzero. Furthermore, we extract the valence quark transverse momentum-dependent parton distributions (TMDs) and generalized parton distributions (GPDs) from their corresponding GTMDs. Additionally, we compute the valence quark electromagnetic form factors (FFs) and parton distribution functions (PDFs) up to twist-$4$. The elastic charge radius of the pion is determined to be $0.558$ fm. Our results exhibit a qualitative agreement with predictions from other theoretical model like Nambu-Jona-Lasinio model, Light-front holographic model, and spectator model at the leading twist. This study provides a comprehensive insight into the internal structure of the pion.